How do I solve 5y - 1 = 3y + 2?

Mathematics

1 answer:

trasher [3.6K]3 years ago

4 0

Answer:

5y - 1 = 3y + 2

2y = 3

y = 1.5

Step-by-step explanation:

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In the diagram below, RSTU is a rectangle, and the two shaded regions are squares.

sdas [7]

Answer:

length PQ = 8.9 m

Step-by-step explanation:

The picture below completes the question you asked. From the picture above RSTU is a rectangle . The two shaded square has a length of sides 8 m and 4 m respectively. The legs of the triangle is the sides of the 2 squares. Therefore, the triangle is a right angle triangle. The adjacent side is 4 m while the opposite side is 8 m.

Using Pythagoras theorem the hypotenuse of the triangle can be calculated below.

Pythagoras theorem

c² = a² + b² Therefore,

c² = 4² + 8²

c² = 16 + 64

c² = 80

square root both sides

c = √80

c = 8.94427191

c ≈ 8.9 m

length PQ = 8.9 m

7 0

4 years ago

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref

Mazyrski [523]

Answer:

7.85 km

Step-by-step explanation:

Let x represent the distance from the refinery to point P. Then the distance under the river from point P to the storage tanks is ...

√(2² +(9 -x)²) = √(x² -18x +85)

In units of $200,000, the cost of the pipeline will be ...

c = x + 2√(x² -18x +85)

The derivative with respect to x is ...

dc/dx = 1 +(2x -18)/√(x² -18x +85)

When we set this to zero, we can get the equation ...

√(x² -18x +85) +(2x -18) = 0

And this can be rewritten as ...

3x^2 -54x +239 = 0

which has solution

x = 9 -(2/3)√3 ≈ 7.8453

Point P should be located about 7.85 km from the refinery.

_____

It is interesting to note that the angle the pipe makes with the riverbank is given by arccos(1/2), where the 1/2 is the ratio of overland to under-river costs. That angle is 60°, so the distance along the riverbank from the storage facility to point P is 2cot(60°) = (2/3)√3 ≈ 1.1547 km. You will recognize this as the value subtracted from 9 km in the solution above.

This "angle solution" is the generic solution to this sort of problem where the route costs are different and part of the route is along the edge of the higher-cost path.